# Mathematics and Computational Thinking

## MCT 121: Mathematics 7

Focusing on algebra and geometry, this course is designed to create the transition from basic number operations to more complex mathematical problems. The course begins with topics that involve whole numbers, fractions, real numbers, and arithmetic, and connects these concepts with simple algebraic expressions and real-life word problems. Students are then introduced to rates, ratios and percentages, applying the algebra they learnt earlier to more complex word problems. In the geometry portion of the course, the students explore angles, triangles and polygons as well as the area, volume and surface area of simple geometric shapes.

Prerequisites: Department consent

## MCT 221 Mathematics 8

This course is designed to lay the foundations of first year algebra and geometry. The algebra topics of study include equations, proportions and inequalities in one variable, writing, solving and graphing linear equations and systems of linear equations, operations involving polynomials, fractions and exponents, factoring and solving quadratic equations, and data analysis. In the geometry portion of the course, constructions, investigations, proofs and projects are used to explore the various facets of geometry. Upon completion of the course, students should have a firm grasp of Euclidean geometry.

Prerequisites: Completion of Math 7 and department consent

## MCT 201: Algebra I

This is a course in first-year algebra with a focus on numerical, algebraic, graphing and verbal methods of problem-solving. The algebra topics of study include equations, proportions, and inequalities in one variable, writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, fractions, exponents and data analysis. Following Algebra I, students take either Integrated Mathematics or Geometry.

Prerequisites: Department consent

## MCT 301: Geometry

The Geometry course is designed to provide a solid foundation of basic and fundamental algebraic and geometric concepts. Upon completion of the course, students should have a firm and confident grasp of Euclidean geometry and be well prepared for further study in mathematics, namely Algebra II and beyond. Constructions, investigations, proofs and projects are used to explore the various facets of geometry. The topics include both inductive and deductive reasoning, and plane, spatial, coordinate, and transformational geometry.

Prerequisites: Department consent

## MCT 321: Integrated Mathematics

Covering all major topics of algebra and geometry, Integrated Mathematics is the foundation for all higher-level math courses. It enables students from a range of math backgrounds to tackle challenging problems with a variety of approaches and to improve their critical thinking skills. The algebra topics of study include writing, solving and graphing linear equations and inequalities, solving and graphing systems of linear equations, operations involving polynomials and factoring, solving quadratic equations, and exponents and radicals, while the geometry topics of study include the properties of lines in a plane, triangles, polygons, similar polygons and right triangles including trigonometric ratios, circles, area and volume.

Prerequisites: Department consent

## MCT 421: Algebra II

Fundamental to the study of advanced Algebra is the thorough development of the concept of functions. Course material includes an emphasis on slope as an average rate of change, introduction of inverse functions, exponential and logarithmic functions, polynomial functions, rational expressions and functions, radical expressions and functions, the introduction of imaginary numbers, right triangle trigonometry and matrices, and an overview of statistics and probability. A graphing calculator is required.

Prerequisites: Completion of Algebra I and Geometry or Integrated Mathematics

## MCT 422: Accelerated Algebra II

Accelerated Algebra includes conic sections, series and sequences and partial fractions along with all Algebra II topics (linear functions and systems, matrices, quadratic and polynomial functions, exponential and logarithmic functions, radical and rational functions, right triangle trigonometry and probability and statistics) with particular emphasis on challenging word problems and applications of the concepts. This course is an excellent choice for students who want to enhance and develop furthermore their critical thinking and problem-solving skills and prepare well for the Accelerated Pre-Calculus course the year after. A graphing calculator is required.

Prerequisites: Completion of Algebra I and Geometry or Integrated Mathematics and department consent

## MCT 501: Functions, Statistics and Trigonometry (FST)

Designed to supplement the material presented in Algebra II, FST completes the study of the elementary functions; linear, quadratic, exponential, logarithmic and trigonometric. Additionally, the course develops some material from finite mathematics including an introduction to probability and statistics, additional applications of trigonometry, and sequences and series. The topics cover a wide range of mathematics and are designed to significantly enhance students' ability to undertake the study of advanced statistical applications. Throughout the entire course, modeling of real phenomena is emphasized. A graphing calculator is required.

Prerequisites: Algebra II and department consent

## MCT 511: Introductory Statistics

From opinion polls and customer satisfaction surveys to drug trials, people seem to be surrounded by data everywhere. The importance of statistical literacy has been steadily increasing over the years, and data analyses often drive decision-making. Thus, students taking this course will rarely question the relevance of course content to real life. Introductory Statistics is primarily a project-based course in which students often collect and analyze their own data. They study proper collection and inference techniques to determine the significance of the data they collected. Students also learn how to build probability models by observing data and design experiments to reduce variability. A graphing calculator is required.

Prerequisites: Functions, Statistics and Trigonometry or Pre-Calculus and department consent

## MCT 521: Pre-Calculus

Pre-Calculus is not a specific, discrete study in mathematics, but rather a course that focuses upon establishing the student's knowledge and skills in preparation for undertaking more advanced math studies. While many of the topics introduced in Algebra II are revisited, they are covered in greater depth and breadth. Included are more challenging studies in functions, analysis of their domains and ranges, recognition of families of curves and their transformations, the study of conic sections, advanced trigonometry, arithmetic and geometric series, and statistics and probability. A graphing calculator is required and integral to the course as methods of solution include algebraic, numeric and graphical approaches.

Prerequisites: Algebra II, Accelerated Algebra II or FST, and department consent

## MCT 522: Accelerated Pre-Calculus

Accelerated Pre-Calculus consolidates algebra and geometry skills, and emphasizes application and synthesis of those topics as a preparation for AP Calculus. The topics include solving algebraic equations and inequalities, function operations, polynomial and rational function analysis, exponential and logarithmic functions, trigonometric functions and applications, sequences and series, and conic sections. Problems are solved numerically, graphically and algebraically, and a graphing calculator is used extensively for modeling and analyzing functions.

Prerequisites: Accelerated Algebra II and department consent

## MCT 552: Introduction to Python Programming

This introductory-level course is for students new to programming and computer science. It emphasizes computational thinking and helps develop the ability to solve complex problems. The course covers the basic building blocks of programming along with other central elements of computer science. It gives a foundation in the tools used in computer science and prepares students for further study in computer science, including Advanced Computer Science Principles and Advanced Computer Science courses.

Course length: One semester

## MCT 621: Calculus

This course covers all of the first semester as well as some of the second semester topics of a college-level calculus survey course. Included are studies in limits and continuity, derivatives and integrals and selected applications of them and an introduction to differential equations. Pre-Calculus topics are reviewed when appropriate to ensure contextual presentation of new material. A graphing calculator is required.

Prerequisites: Pre-Calculus and department consent

## MCT 651: Advanced Computer Science Principles

Advanced Computer Science Principles introduces students to the central ideas of computer science, instilling the ideas and practices of computational thinking and inviting students to understand how computing changes the world. The rigorous course promotes deep learning of computational content, develops computational thinking skills, and engages students in the creative aspects of the field. The course is unique in its focus on fostering creativity in students. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using simulations to explore questions that interest them. Rather than teaching a particular programming language or tool, the course focuses on using technology and programming as a means to solve computational problems and create exciting and personally relevant artifacts. Students design and implement innovative solutions using an iterative process similar to what artists, writers, computer scientists and engineers use to bring ideas to life. This course prepares students for the AP Computer Science Principles exam as well as the assessment that asks students to explore the implications of computing innovations and create a computer application.

Prerequisites: Department consent. No prior computer science knowledge or experience is necessary

This course follows the College Board Advanced Placement syllabus and is designed to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad-conceptual themes: exploring data (describing patterns and departures from patterns), sampling and experimentation (planning and conducting a study), anticipating patterns (exploring random phenomena using probability and simulation) and statistical inference (estimating population parameters and testing hypotheses). A graphing calculator is required. After the completion of this course, students are expected to take the AP Statistics Exam.

Prerequisites: Pre-Calculus, Accelerated Pre-Calculus, or Functions, Statistics and Trigonometry and department consent

## MCT 721: Advanced Calculus I

A rigorous and challenging course comparable to courses in colleges and universities, Advanced Calculus I is designed for students with excellent mathematical skills who seek college credit, college placement or both from institutions of higher learning. Based on the College Board Advanced Placement AB syllabus, the course approaches the calculus concepts (limits and continuity, derivatives and integrals and their applications) from multiple perspectives — graphically, analytically, numerically and verbally. A graphing calculator is required. After the completion of this course, students are expected to take the AP Calculus AB Exam.

Prerequisites: Pre-Calculus or Accelerated Pre-Calculus and department consent

## MCT 722: Advanced Calculus II

Designed as an extension of Advanced Calculus I rather than an enhancement, Advanced Calculus II includes, along with all Advanced Calculus I topics, additional topics such as: integration by parts and by tables, improper integrals, Euler’s Method and L’Hôpital’s Rule, infinite series, parametric equations, and polar coordinates and polar graphs. A graphing calculator is required. After the completion of this course, students are expected to take the AP Calculus BC Exam.

Prerequisites: Accelerated Pre-Calculus or Advanced Calculus I and department consent

## MCT 752: Advanced Computer Science

This course is based on the College Board AP Computer Science A syllabus which is equivalent to the first semester of a college level computer science course. The course develops the skills to write programs or part of programs to correctly solve specific problems. It also emphasizes the design issues that make programs understandable, adaptable and when appropriate, reusable. At the same time, the development of useful computer programs and classes is used as a context for introducing other important concepts in computer science, including the development and analysis of algorithms, the development and use of fundamental data structures and the study of standard algorithms and typical applications. In addition, an understanding of the basic hardware and software components of computer systems and the responsible use of these systems are integral parts of the course. The course uses Java as a tool to teach the methodology of object-oriented programming and problem-solving techniques through the development and usage of algorithms.

Prerequisites: Introduction to Programming or its equivalent and department consent

## MCT 821: Multivariable Calculus

Unlike Advanced Calculus I and II in which students study calculus of a single variable, Multivariable Calculus, a rigorous college course, focuses on functions of two or more independent variables. The concepts studied in this course are applied in many different fields — thermodynamics, electricity and magnetism, economics, modeling fluid or heat flow, etc. The topics included are vectors and the geometry of space, vector-valued functions, functions of several variables, multiple integration, vector analysis, and second order differential equations. A graphing calculator is required.